Abstract
Representations of the Lie algebra su(1,1) and of a generalization of the oscillator algebra, b(1), are considered. The paper then introduces polynomials which are related by the coupling (or Clebsch–Gordan) coefficients of the Lie algebra in question; by making a proper choice, these polynomials themselves are related to known special functions. The coupling of two or three representations of the Lie algebra then leads to interesting addition formulas for these special functions. The polynomials appearing here are generalized Laguerre and Jacobi polynomials for the su(1,1) case, and Hermite polynomials for the b(1) algebra.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
